In a Couette flow, two large flat plates lie one atop another, separated by a thin layer of fluid. If a shear stress is applied to the top plate, the viscosity of the fluid produces motion in the bottom plate as well. The velocity V in the top plate relative to the bottom plate is given by V = τh/μ, where τ is the shear stress applied to the top plate, h is the thickness of the fluid layer, and μ is the viscosity of the fluid. Assume that μ, h, and τ are measured independently and that the measurements are unbiased and normally distributed. The measured values are μ = 1.6Pa · s, h = 15 mm, and τ = 25 Pa. The uncertainties (standard deviations) of these measurements are σμ = 0.05, σh = 1.0, and στ = 1.0.
a. Use the method of propagation of error to estimate V and its uncertainty σV.
b. Assuming the estimate of V to be normally distributed, find a 95% confidence interval for V.
c. Perform a simulation to determine whether or not the confidence interval found in part (b) is valid?